Ballscrew Force Calculator
Convert between motor torque and linear force. Results update in real-time.
Calculation Mode
Enter motor torque to calculate linear force output.
Screw Type
Motor Torque
Typical NEMA 23: 1–3 Nm · NEMA 34: 3–12 Nm
Typical CNC axis force: 200–2000 N
Calculated Results
Linear Force
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N
Force in kgf
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Force in lbf
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Formula used
F = (2π × T × η × 1000) / Lead
Worked Example
Problem: A NEMA 23 stepper motor with 1.26 Nm of holding torque drives a ballscrew with a 5 mm lead. How much linear force can the axis produce?
Given: T = 1.26 Nm, Lead = 5 mm, η = 0.9 (ballscrew)
F = (2π × 1.26 × 0.9 × 1000) / 5
F = (6.2832 × 1.26 × 0.9 × 1000) / 5
F = 7124.7 / 5
F = 1424.9 N (145.3 kgf / 320.3 lbf)
This means the axis can push or pull with approximately 1425 N of force. For reference, cutting aluminum on a hobby CNC typically requires 100–500 N of force, so this motor/screw combination has plenty of margin.
Frequently Asked Questions
What is a ballscrew lead?
The lead is the linear distance the nut travels per one full revolution of the screw shaft, measured in mm/rev. Common leads are 5 mm, 10 mm, and 20 mm. A higher lead gives faster travel speed but less force multiplication.
Ballscrew vs. rolled screw vs. ACME — what is the difference?
Ballscrews use recirculating ball bearings for very low friction (90% efficiency). Rolled screws are a budget alternative with slightly lower precision and efficiency (80%). ACME/trapezoidal screws use sliding contact, resulting in much higher friction (40% efficiency) but they are the cheapest option and offer self-locking, which can be useful for vertical axes.
Why does efficiency matter?
Efficiency (η) represents how much of the motor's rotational energy is converted into useful linear force. A ballscrew at 90% efficiency converts most of the torque into force, while an ACME screw at 40% efficiency loses more than half to friction. This directly affects how much force your axis can produce and how much heat is generated.
How much force do I need for CNC routing?
It depends on the material and cutting parameters. Routing wood typically requires 50–200 N of cutting force. Aluminum can require 200–800 N depending on depth of cut and feed rate. A good rule of thumb is to have at least 3x the expected cutting force as your axis capacity to maintain rigidity and accuracy under load.
Does a higher lead always mean less force?
Yes. The screw lead acts as a gear ratio. A 5 mm lead gives twice the force of a 10 mm lead for the same motor torque, but the 10 mm lead moves twice as fast. You must balance speed and force requirements for your application. Most hobby CNC machines use 5 mm or 10 mm lead ballscrews.